Question: Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{n^2 + 6n}{n^2 + n - 30}$
Solution: First factor the expressions in the numerator and denominator. $ \dfrac{n^2 + 6n}{n^2 + n - 30} = \dfrac{(n)(n + 6)}{(n - 5)(n + 6)} $ Notice that the term $(n + 6)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n + 6)$ gives: $x = \dfrac{n}{n - 5}$ Since we divided by $(n + 6)$, $n \neq -6$. $x = \dfrac{n}{n - 5}; \space n \neq -6$